Find the general solution of the differential equations dxdy+y=1(y=1)
Let y(x) be a solution of the differential equation (1+ex)yprime+yex=1. If y(0)=2 , then which of the following statements is (are) true? (a)y(−4)=0 (b)y(−2)=0 (c)y(x) has a critical point in the interval (−1,0) (d)y(x) has no critical point in the interval(−1,0)
A body at a temperature of 500F is placed outdoors where the temperature is 1000F . If the rate of change of the temperature of a body is proportional to the temperature difference between the body and its surrounding medium. If after 5 min the temperature of the body is 600F , find (a) how long it will take the body to reach a temperature of 75 0 F and (b) the temperature of the body after 20 min.
If for the differential equation y′=yx+ϕ(xy), the general solution is y=xlog|Cx|, then ϕ(x/y) is given by
The population of a country doubles in 40 years. Assuming that the rate of increase is proportional to the number of inhabitants, the number of years in which it would treble itself is